Marked point process learning with applications to modelling and forecasting of earthquakes and ambulance calls

This project proposes the first supervised statistical learning framework for general marked point processes (MPPs) which are generalised random samples, with random samples sizes, consisting of input-output pairs (events) which we allow to be dependent of each other. This makes MPPs particularly suited for modelling spatial and/or temporal event phenomena.

A motivator has been spatio-temporal modelling and forecasting of earthquakes and ambulance call characteristics, where an input is a spatial location and a time stamp (and external covariates), and an output is a magnitude/call characteristics.Supervised learning, which deals with prediction of outputs using inputs through a fitted model, has classically assumed a fixed number of independent and identically distributed events.

The proposed methodology generalises this to the MPP setting by introducing two new concepts for MPPs: i) cross-validation, which splits the data/MPP and allows us to do conditional repeated sampling, and ii) prediction errors, which allow us to measure how well a given model can predict one part of a split using the other one.We i) propose new (neural network-based) model forms for MPPs, which collect existing model formulations under one powerful umbrella; ii) propose and explore a new framework for supervised learning for MPPs, with focus on both theoretical development and applications; iii) propose and explore a new forecasting algorithm for spatio-temporal models.